Power spectrum slope confounds estimation of instantaneous oscillatory frequency

Abstract

Oscillatory neural dynamics are highly non-stationary and require methods capable of quantifying time-resolved changes in oscillatory activity in order to understand neural function. Recently, a method termed ‘frequency sliding’ was introduced to estimate the instantaneous frequency of oscillatory activity, providing a means of tracking temporal changes in the dominant frequency within a sub-band of field potential recordings. Here, the ability of frequency sliding to recover ground-truth oscillatory frequency in simulated data is tested while the exponent (slope) of the 1/fx component of the signal power spectrum is systematically varied, mimicking real electrophysiological data. The results show that 1) in the presence of 1/f activity, frequency sliding systematically underestimates the true frequency of the signal, 2) the magnitude of underestimation is correlated with the steepness of the slope, suggesting that, if unaccounted for, slope changes could be misinterpreted as frequency changes, 3) the impact of slope on frequency estimates interacts with oscillation amplitude, indicating that changes in oscillation amplitude alone may also influence instantaneous frequency estimates in the presence of strong 1/f activity; and 4) analysis parameters such as filter bandwidth and location also mediate the influence of slope on estimated frequency, indicating that these settings should be considered when interpreting estimates obtained via frequency sliding. The origin of these biases resides in the output of the filtering step of frequency sliding, whose energy is biased towards lower frequencies precisely because of the 1/f structure of the data. We discuss several strategies to mitigate these biases and provide a proof-of-principle for a 1/f normalization strategy.